Sunday, 29 December 2013

integration - Finding the integral intp0ifracdtheta(2+costheta)2 by complex analysis

Trying to find the integral π0dθ(2+cosθ)2

by complex analysis.



I let z=exp(iθ), dz=iexp(iθ)dθ, so dθ=dziz. I am trying therefore to find the integral 12izCdz(2+z2+12z)2

I am unsure of which contour I should use, and how to proceed besides that. Could anyone help?

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